數字信號處理a雙語chapter6ztransa140404

1、上講回顧上講回顧lz變換的定義：變換的定義：lz變換和變換和dtft的關系：的關系：lz平面和收斂域平面和收斂域nnzngzg)( )() jjj nz eng zg eg n e z 變換收斂域的特點：變換收斂域的特點：l收斂域是一個圓環(huán)，有時可向內收縮到原點收斂域是一個圓環(huán)，有時可向內收縮到原點有時可向外擴展到有時可向外擴展到，只有序列，只有序列(n)的收斂域的收斂域是整個是整個z平面平面l收斂域內無極點，收斂域內無極點，x(z)在收斂域內每一點上在收斂域內每一點上都是解析函數。都是解析函數。lz 變換表示法：級數形式、解析表達式變換表示法：級數形式、解析表達式 （注意（注意:函數收斂域，

2、缺一不可）函數收斂域，缺一不可）chapter 6z-transformchapter 6 z-transformlpart a: z-transformlpart b: the inverse z-transform and z-transform theoremslpart c: convolution(卷積卷積) lpart d: the transfer functionlintroductionl6.1 definitionl6.2 rational z-transforms(有理有理z變換變換)l6.3 region of convergence（收斂域）（收斂域） of a ra

3、tional z-transform part a: z-transformpart a: introductionlthe dtft provides a frequency-domain (頻域頻域) representation of discrete-time signals and lti（線（線性時不變）性時不變）discrete-time systems.lbecause of the convergence condition, in many cases, the dtft of a sequence may not exist.las a result, it is not

4、 possible to make use of such frequency-domain characterization in these cases.part a: introductionlin general, zt can be thought of as a generalization of the dtft. zt is more complex than dtft (both literally and figuratively), but provides a great deal of insight into system design and behavior.

5、lfor discrete-time systems, zt plays the same role of laplace-transform does in continuous time systems. zt characterizes signals or lti systems in complex frequency domain（復頻域）（復頻域）.6.1 definition of z-transform6.1 definition of z-transform6.1 definition of z-transform6.1 definition of z-transform6

6、.1 definition of z-transform6.1 definition of z-transform6.1 definition of z-transform6.1 definition of z-transform6.1 definition of z-transform6.1 definition of z-transform6.1 definition of z-transform6.1 definition of z-transformimzjrez0平面zaz a6.1 definition of z-transform imzjrez0平面zaz a6.1 defin

7、ition of z-transformtable 6.1 some commonly used z-transform pairslintroductionl6.1 definitionl6.2 rational z-transforms(有理有理z變換變換)l6.3 region of convergence（收斂域）（收斂域） of a rational z-transform part a: z-transform6.2 rational z-transform6.2 rational z-transform6.2 rational z-transform6.2 rational z-

8、transform6.2 rational z-transform6.2 rational z-transform6.2 rational z-transform6.2 rational z-transforml零極點共軛成對出現、收斂域內無極點零極點共軛成對出現、收斂域內無極點l需注意的是：求解零、極點時，為避免遺漏，需注意的是：求解零、極點時，為避免遺漏，需需先將先將z變換有理分式的分子和分母都轉換成變換有理分式的分子和分母都轉換成z的正數次冪的正數次冪，再進行求解，詳見第，再進行求解，詳見第26頁頁ppt。11()1x zaz zza lintroductionl6.1 definiti

9、onl6.2 rational z-transforms(有理有理z變換變換)l6.3 region of convergence（收斂域）（收斂域） of a rational z-transform part a: z-transform6.3 region of convergence of a rational z-transform6.3 region of convergence of a rational z-transform6.3 region of convergence of a rational z-transform6.3 region of convergence

10、of a rational z-transform6.3 region of convergence of a rational z-transform有限長序列的有限長序列的z變換變換有限長序列的有限長序列的z變換變換例例1：序列：序列x（n）=（n）的）的z變換變換 由于由于n1=n2=0，其收斂域為整個閉域，其收斂域為整個閉域 z平面，平面，0|z|0( )( )11nnx zn zz 例例2：矩形序列：矩形序列x（n）=rn（n） 有限項等比級數求和有限項等比級數求和 112(1)0( )( )11nnnnnnnx zrn zzzzz 11( ), 0|1nzxzzz 0(1)1naq

11、q 6.3 region of convergence of a rational z-transform6.3 region of convergence of a rational z-transformz變換的收斂域包括變換的收斂域包括 點是因果序列的特征。點是因果序列的特征。6.3 region of convergence of a rational z-transform6.3 region of convergence of a rational z-transform6.3 region of convergence of a rational z-transform6.3 r

12、egion of convergence of a rational z-transform6.3 region of convergence of a rational z-transform6.3 region of convergence of a rational z-transform6.3 region of convergence of a rational z-transform6.3 region of convergence of a rational z-transform6.3 region of convergence of a rational z-transformwherellllllaaabbbaaabbbaaabbbsos2102102212022212021211012111012211